/*=====================================================================*
 *                   Copyright (C) 2011 Paul Mineiro                   *
 * All rights reserved.                                                *
 *                                                                     *
 * Redistribution and use in source and binary forms, with             *
 * or without modification, are permitted provided that the            *
 * following conditions are met:                                       *
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 *     * Redistributions of source code must retain the                *
 *     above copyright notice, this list of conditions and             *
 *     the following disclaimer.                                       *
 *                                                                     *
 *     * Redistributions in binary form must reproduce the             *
 *     above copyright notice, this list of conditions and             *
 *     the following disclaimer in the documentation and/or            *
 *     other materials provided with the distribution.                 *
 *                                                                     *
 *     * Neither the name of Paul Mineiro nor the names                *
 *     of other contributors may be used to endorse or promote         *
 *     products derived from this software without specific            *
 *     prior written permission.                                       *
 *                                                                     *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND              *
 * CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES,         *
 * INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES               *
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE             *
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER               *
 * OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,                 *
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 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE           *
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 * Contact: Paul Mineiro <paul@mineiro.com>                            *
 *=====================================================================*/

#ifndef __NORMALIZE_HH__
#define __NORMALIZE_HH__

#include <vector>

#include "fastonebigheader.hh"

namespace playerpiano
{

float
safe_exponentiate_normalize (std::vector<float>& xvec)
{
  /*
   * ok we want to compute 
   * 
   *            exp (x[i])          exp (x[i] - max)
   * x[i] = ----------------- = ------------------------
   *        sum_i exp (x[i])     sum_i exp (x[i] - max)
   *
   * the RHS is more numerically stable
   */

  float* x = &xvec[0];
  unsigned int n = xvec.size ();

  unsigned int maxindex = 0;

  for (unsigned int i = 1; i < n; ++i)
    {
      if (x[i] > x[maxindex])
        {
          maxindex = i;
        }
    }

  float denominator = 0;
  float max = x[maxindex];

  for (unsigned int i = 0; i < n; ++i)
    {
      x[i] = fastexp (x[i] - max);
      denominator += x[i];
    }

  float q = 0;
  for (unsigned int i = 0; i < n; ++i)
    {
      x[i] /= denominator;
      q -= (x[i] > 0) ? x[i] * fastlog (x[i]) : 0;
    }

  return q;
}

void
safe_normalize (std::vector<float>& xvec)
{
  /*
   * ok we want to compute 
   *
   * x[i] = x[i] - log (sum_i exp (x[i]))
   *
   *      = x[i] - max - log (sum_i exp (x[i] - max))
   * 
   * the second expression is more numerically stable
   */

  float* x = &xvec[0];
  unsigned int n = xvec.size ();

  unsigned int maxindex = 0;

  for (unsigned int i = 1; i < n; ++i)
    {
      if (x[i] > x[maxindex])
        {
          maxindex = i;
        }
    }

  float denominator = 0;
  float max = x[maxindex];

  for (unsigned int i = 0; i < n; ++i)
    {
      denominator += fastexp (x[i] - max);
    }

  denominator = fastlog (denominator);

  for (unsigned int i = 0; i < n; ++i)
    {
      x[i] -= max;
      x[i] -= denominator;
    }
}

}

#endif /* __NORMALIZE_HH__ */
